We implement our method on PyMARL [1]} and use 10 random seeds to train each method on all environments. We use opensourced code of baselines publicly by the corresponding authors on Github in all experiments. We use the default settings of PyMARL in our research, including the relay buffer, the mixing network, the training hyperparameters. In order to explore, we use \(\epsilon \) -greedy with \(\epsilon \)  annealed linearly from 1.0 to 0.05 over 50K time steps from the start of training and keep it constant for the rest of the training for all methods. The discount factor \(\gamma =0.99\)  and we follow the default hyper-parameters used in the original papers of all methods in our research. We carry out experiments on NVIDIA A100 Tensor Core GPU and NVIDIA GeForce RTX 3090 24G. We resort to mean-std values as our performance evaluation measurement. We use \(\beta =0.00001\)  in Eqn. REF . To create sub-graphs in LeGEM, we first calculate the episode return and keep 1 decimal of it. We then use this episode return to create each sub-graph. We list some important hyper-parameters in Tab. REF .
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